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We describe a quantum error-detecting and error-correcting code embeddedwithin irreducible representations of SU(3). These logical qutrits inherit theHe(3) symmetries induced by the representation, while protecting against smallSU(3) displacements. We explore the general methodology for finding codes fromstructure-inducing representations of groups, together with symmetriesinherited from finite subgroups, extending the case of spin representations ofSU(2).

Qutrit codes within representations of SU(3)